title: An estimation of generalized bradley-terry models based on the em algorithm.
abstract: The Bradley-Terry model is a statistical representation for one's preference or ranking data by using pairwise comparison results of items. For estimation of the model, several methods based on the sum of weighted Kullback-Leibler divergences have been proposed from various contexts. The purpose of this letter is to interpret an estimation mechanism of the Bradley-Terry model from the viewpoint of flatness, a fundamental notion used in information geometry. Based on this point of view, a new estimation method is proposed on a framework of the em algorithm. The proposed method is different in its objective function from that of conventional methods, especially in treating unobserved comparisons, and it is consistently interpreted in a probability simplex. An estimation method with weight adaptation is also proposed from a viewpoint of the sensitivity. Experimental results show that the proposed method works appropriately, and weight adaptation improves accuracy of the estimate.
authors.affiliation: Department of Integrated Information Technology, Aoyama Gakuin University, Chuo, Sagamihara, Kanagawa 252-5258, Japan. yu.fujimoto@it.aoyama.ac.jp
authors.forename: Yu
authors.initials: Y
authors.lastname: Fujimoto
authors.forename: Hideitsu
authors.initials: H
authors.lastname: Hino
authors.forename: Noboru
authors.initials: N
authors.lastname: Murata
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D012044:Regression Analysis